This study demonstrates the existence of stationary solutions for the three-dimensional fractional Navier-Stokes-Coriolis system in critical Fourier-Besov Morrey spaces. Initially, the focus is on the non-stationary fractional Navier-Stokes-Coriolis system, and the existence of stationary solutions is then established within this framework. In addition, the study outlines a form of stability for these non-stationary solutions, which when applied to the stationary case, leads to the conclusion that, under appropriate conditions, non-stationary solutions converge to the stationary ones as time approaches infinity. Finally, a relationship between the external force and the Coriolis parameter is established to obtain a unique solution for the stationary system.